The efficiency of competitive equilibria in insurance markets with asymmetric information

doi:10.1016/0047-2727(85)90005-2

Journal of Public Economics

Volume 26, Issue 2, March 1985, Pages 207-219

https://doi.org/10.1016/0047-2727(85)90005-2 Get rights and content

Abstract

This paper addresses the relationship between competitive equilibria and efficient allocations in an insurance market with asymmetric information. Using the definition of second-best efficiency proposed by Harris and Townsend (1981) for environments characterized by informational assmmetry, the efficiency properties of several proposed market equilibria are examined. We find an analogue to the First Optimality Theorem: A Miyazaki-Wilson equilibrium always results in a second best allocation.

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A simple tax structure for competitive equilibrium and redistribution in insurance markets with asymmetric information
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There are more references available in the full text version of this article.

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This article studies general economies with adverse selection in which symmetric companies supply (potentially multiple) plans to privately informed consumers and compete in terms of price schedules. I show that a basic price cap regulation, in which the price caps are endogenously determined by companies, discourages risk selection over efficient allocations, and therefore, equilibrium exists in every economy. Moreover, I demonstrate that in generalisations of Rothschild and Stiglitz (1976) and Wilson (1977) economies, companies earn zero profits in equilibrium, and every equilibrium allocation is efficient.
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Instead, the MWS equilibrium concept resolves the tension in favor of the second competitive force, yielding market equilibria which are constrained efficient but (may) involve cross subsidies across contracts.23 Concepts in both veins have been widely employed for studying competitive markets with adverse selection in markets with small, finite type spaces (including Hoy (1982), Crocker and Snow (1985), Puelz and Snow (1994), Crocker and Snow (2008), Finkelstein et al. (2009), and Mimra and Wambach (2019b) for the MWS concept, and Besanko and Thakor (1987), Landers et al. (1996), Newhouse (1996), Inderst (2005), Handel et al. (2015), Boyer and Peter (2020), and Mimra and Wambach (2019b) for the AG/Riley concept). But adjudicating which concept is appropriate for empirical applications, and in what circumstances, calls for tractable models with richer type spaces.
We prove the existence of the constrained efficient Miyazaki (1977)–Wilson (1977)–Spence (1978) equilibrium in competitive markets with adverse selection when the distribution of unobservable types is continuous. Our existence proof applies under extremely general assumptions about individual preferences. When we restrict preferences to have the widely-used-in-the-selection-markets-literature quasilinear form, we characterize the properties of this equilibrium by developing a simple and computationally efficient numerical method for constructing it. Applying this method, we show in a natural setting how one would compute the equilibrium allocation, potentially facilitating empirical work using the MWS equilibrium. We illustrate this empirical application in the context of policy interventions and show that the welfare implications of a coverage mandate critically hinge on whether the market implements a constrained efficient allocation like the MWS equilibrium or a constrained inefficient allocation like in Azevedo and Gottlieb (2017).
Optimal ex post risk adjustment in markets with adverse selection
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Second, the set of efficient allocations is potentially large. For instance, in the simple two-by-two insurance market studied in Rothschild and Stiglitz (1976), in which there are two possible states (accident and no accident) and two possible types (high risk and low risk), the set of efficient allocations as characterised in Crocker and Snow (1985) consists of a continuum of allocations. Some allocations involve cross-subsidies and, hence, are vulnerable to risk selection.
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^∗: The authors wish to thank Maxim Engers and members of the Microeconomics Workshop of the University of Virginia for helpful comments on an earlier version of this paper.

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The efficiency of competitive equilibria in insurance markets with asymmetric information

Abstract

Journal of Public Economics

Journal of Economic Theory

Towards a solution to the general problem of self-selection

Multiperiod insurance contracts

Vertical integration and the strategic use of private information

Bell Journal of Economics

The desirable welfare effects of categorizing risks in the insurance industry

A simple tax structure for competitive equilibrium and redistribution in insurance markets with asymmetric information

Southern Economic Journal